This, and the other problems you have posted, can all be done using one or more of the following:

Bob

]]>http://www.mathisfunforum.com/profile.php?id=676942012-12-05T18:55:04Zhttp://www.mathisfunforum.com/viewtopic.php?pid=242695#p242695YES, and although it wants to make sense, its is bouncing between my ears unclear when I try to apply. Ive been trying to short cut the process to come close to an answer.]]>http://www.mathisfunforum.com/profile.php?id=1958032012-12-05T18:42:40Zhttp://www.mathisfunforum.com/viewtopic.php?pid=242693#p242693Hi gbrad88

Have you read noelevans post (post #3 in this thread)?

]]>http://www.mathisfunforum.com/profile.php?id=1187862012-12-05T18:01:57Zhttp://www.mathisfunforum.com/viewtopic.php?pid=242689#p242689Whew, I don't know. This is the upper limit of my ability and understanding. This is my final unit in my semester and this was a very bad unit for me. Thankfully my grades were high enough up to this point, but Im really hitting the wall on understanding the log, ln, all of that.]]>http://www.mathisfunforum.com/profile.php?id=1958032012-12-05T17:05:13Zhttp://www.mathisfunforum.com/viewtopic.php?pid=242686#p242686Hi! I hope you have had a chance to try stefy's suggestion and solved the problem. If not, thengive it a try before looking at the following proof of the rule involved in solving the problem.

The definition of log is usually introduced via two equalities in two variables, namely, x N = 10 and x = logN which somewhat obscures the meaning of the logarithm.

logNIf we substitute logN for x in the first equality we get N = 10 ("lay on goodies" to get N.)which gives us a single equality with a single variable. And from this single equality we canbasically read the definition of logN: "logN is the exponent we must apply to 10 to get N."logN is a NAME for the right exponent that applied to 10 produces N. So logs are names forexponents. And the naming is nice in that it tells us what the base is that it must be applied toand the result we get when we apply it to that base. If the base is b then the logarithm is log N b log N which when applied to base b results in N; that is, b = N. b

(In Maple the log is written log[b](N).)

logNWriting N as 10 (by the definition of log) we obtain p p logN p p*logN p log(N ) N =(10 ) = 10 by a law of exponents. Also N = 10 by the definition of log. p p( x was immediately above but should have been N left of the equal sign. That's the edit.) p p*logN log(N )Thus 10 = 10 and since the bases are equal and the quantities are equal then pthe exponents must be equal; that is, p*logN = log(N ). (because log is a 1-1 function.)

p pMore generally p*log N = log (N ) so the exponent on N in the argument of log (N ) b b b p"comes out front" forming p*log N. And if b=e then we have p*lnN = ln(N ) b n m nm logN p p*logNThis is a disguised form of the law of exponents: (x ) = x . Here it is (10 ) = 10 .

In the original problem the p=3 for x and the p=1/3 for the y.

Then the difference produces a quotient in the argument of the single logarithm.